Which geometric construction is shown here? a)construct a circle given 3 pointsb)construct the center of a given circlec)construct the orthocenter of a triangled)construct the tangent to a point on the circle

Option: B is the correct answer.

B) Construct the center of a given circle.

Step-by-step explanation:

The center of the circle is constructed as:

Draw a chord AB and construct it's perpendicular bisector.Draw another chord CD and construct it's perpendicular bisector.The point where the perpendicular bisectors of both the chord meet gives us the center of the given circle.

Hence, option B is correct we are given a geometric construction of center of a given circle.

Option B. construct the center of a given circle.

Step-by-step explanation:

To determine the center of a given circle we will follow the following steps

1). We will draw a chord which intersects the circle at A and B.

2). We will construct perpendicular bisector of chord AB.

3). Similarly we will draw another chord CD and construct perpendicular bisector of CD.

4). As we know perpendicular from the center of a circle to any chord, bisects the chord. So we extend the perpendicular bisectors intersecting each other at point E.

Hence the intersection point E will be the center of the circle.

Option B. is the answer.

The exponential growth function is

Step-by-step explanation:

Given : Fiona started her study of bacteria growth with 1,000 bacteria in a Petri dish. After 1 hour, the count was increased to 1,800. After 2 hours, the count was 3,240. After the third hour showed a count of 5,832. Fiona wrote an equation to represent the exponential growth of the bacteria.

To find : What exponential growth function did Fiona write?

Solution :

The general form of an exponential function is ....(1)

Where, a is the initial value and r is the rate factor.

According to question,

Initial value is a=1000

After 1 hour, the count was increased to 1,800.

After 2 hours, the count was 3,240.

After the third hour showed a count of 5,832,

Let x represents the time in hour and y represents thee count of bacteria.

Taking the points (1,1800), (2,3240).

Substitute in equation (1),

  .....(2)

....(3)

Divide equation (3) by (2),

The rate factor is b=1.8

Now, Substitute the value of a and b in equation (1)

Therefore, The exponential growth function is